Probing the Evolution of the Electron Spin Wave Function of the Nitrogen-Vacancy Center in Diamond via Pressure Tuning

Kin On Ho, Man Yin Leung, P. Reddy, Jianyu Xie, King Cho Wong, Yaxin Jiang, Wei Zhang, King Yau Yip, Wai Kuen Leung, Yiu Yung Pang, King Yiu Yu, Swee K. Goh, M.W. Doherty, and Sen Yang

Phys. Rev. Applied 18, 064042 – Published 14 December 2022

Abstract

Understanding the profile of a qubit’s wave function is key to its quantum applications. Unlike conducting systems, where a scanning tunneling microscope can be used to probe the electron distribution, there is no direct method for solid-state-defect-based qubits in wide-band-gap semiconductors. In this work, we use pressure as a tuning method and a nuclear spin as an atomic scale probe to monitor the hyperfine structure of negatively charged nitrogen-vacancy (N- $V$ ) centers in diamonds under pressure. We present a detailed study on the nearest-neighbor $^{13} C$ hyperfine splitting in the optically detected magnetic resonance spectrum of N- $V$ centers at different pressures. By examining the $^{13} C$ hyperfine interaction upon pressurizing, we show that the N- $V$ hyperfine parameters have prominent changes, resulting in an increase in the N- $V$ electron spin density and rehybridization from $s p^{3}$ to $s p^{2}$ bonds. The ab initio calculations of strain dependence of the N- $V$ center’s hyperfine levels are done independently. The theoretical results qualitatively agree well with experimental data without introducing any fitting parameters. Furthermore, this method can be adopted to probe the evolution of wave function in other defect systems. This potential capability could play a role in developing magnetometry and quantum information processing using the defect centers.

Received 14 April 2022
Revised 7 November 2022
Accepted 21 November 2022

DOI:https://doi.org/10.1103/PhysRevApplied.18.064042

Physics Subject Headings (PhySH)

Color centers NV centers Quantum information with solid state qubits

Nitrogen vacancy centers in diamond

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Kin On Ho ^1,‡, Man Yin Leung ^2,‡, P. Reddy^3,‡, Jianyu Xie^1,‡, King Cho Wong ^1,‡, Yaxin Jiang¹, Wei Zhang ¹, King Yau Yip ¹, Wai Kuen Leung ², Yiu Yung Pang¹, King Yiu Yu¹, Swee K. Goh ^1,4, M.W. Doherty^3,*, and Sen Yang ^1,2,†

¹Department of Physics, The Chinese University of Hong Kong, Shatin, New Territories, Hong Kong, China
²Department of Physics and the IAS Centre for Quantum Technologies, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, China
³Laser Physics Centre, Research School of Physics and Engineering, Australian National University, 2601, Australia
⁴Shenzhen Research Institute, The Chinese University of Hong Kong, Shatin, New Territories, Hong Kong, China

^*marcus.doherty@anu.edu.au
^†phsyang@ust.hk
^‡These authors contributed equally to this work.

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Vol. 18, Iss. 6 — December 2022

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Images

Figure 1
(a) Illustration of our DAC. 1- $μ m$ NDs are dropcasted onto one of the anvil culets. 4:1 methanol:ethanol mixture is used as the pressure medium that is confined by a metallic gasket, while two aligned diamond anvils are used for generating pressure. The central hole of the gasket had a diameter of $300 μ m$ . A 150- $μ m$ -diameter $Ω$ -shaped gold microstructure is used as a MW antenna for ODMR measurements. (b) The energy levels of the hyperfine structures. There are two $^{13} C$ ODMR parameters $Δ_{hf}$ and $δ_{hf}$ , which correspond to the separation and center of the two hyperfine resonances, respectively. (c) The ODMR spectra of the same ND at 17.0 and 104.5 kbar. The $f_{offest}$ is defined as the difference from the center frequency $D$ . The pressure-induced changes in hyperfine resonances in the ODMR spectrum upon pressure change could be directly observed. It is obvious that the $^{13} C$ hyperfine resonances have relatively broad linewidths and low contrasts compared to the center resonances. The pressure is determined by the center frequency of the corresponding ODMR spectrum [9].
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Figure 2
Plots of $^{13} C$ ODMR parameters (a) $Δ_{hf} (P)$ and (b) $δ_{hf} (P)$ against pressure. Three NDs are tracked. The joining lines signify the data measurement sequence. The changes in $Δ_{hf}$ and $δ_{hf}$ with pressure are pronounced. The linear fits are the dash lines. The light gray line in the background is the theory result.
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Figure 3
Derived results of (a) hyperfine constant $A_{⊥}$ , (b) hyperfine constant $A_{‖}$ , (c) Fermi contact term $f$ , (d) dipole term $d$ , (e) hybridization of the $p$ orbitals $| c_{p} |^{2}$ , and (f) electron spin density $η$ . The black markers are derived purely from theoretical values. The electron density $η$ increases while the $p$ -orbital contribution $| c_{p} |^{2}$ decreases, both slightly. The green error bound is from the maximum uncertainty of the theoretical resolution of 0.1 kHz/kbar. This theoretical resolution is the smallest energy difference resolvable in our calculations. It mainly affects the terms $d δ_{hf} / d P$ since the neglected hyperfine-stress interaction in $δ_{hf}$ is of the same order. Furthermore, the term $d δ_{hf} / d P$ is shown to be the most sensitive input parameter that impacts the derived results [47]. Note that the theoretical resolution of 0.1 kHz/kbar is much better than the test case of, yet still merely, 0.1% difference (around 1 kHz/kbar).
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Figure 4
Schematic of lattice distortion and the consequent redistribution of spin density between atoms and rehybridization of the atomic orbitals. The arrows indicate the displacements of atoms for increasing pressure. The axes $(X, Z)$ correspond to the crystallographic coordinate system.
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Figure 5
(a) The average $E$ and (b) the SD of the center frequency $D$ verse the average pressure measured by NDs ( $d D / d P = 1.49$ MHz/kbar [9]). The joining lines signify the data measurement sequence. From the insignificant variations in these quantities under applied pressure, we conclude that the mixture is in excellent hydrostatic condition within our pressure range, meaning that the hydrostatic pressure approximation works well.
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Figure 6
An example of the fitting at ambient pressure. Red line is the raw data and green line is the cumulative fit of the four-Lorentzian peaks.
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